AFAIK there's no reason to favor English translations of the Old Testament (or anything else) that use now-archaic English, except maybe for passages which are
themselves written, in the original, in a kind of archaic or very formal mode, relative to the rest. It can be accurate enough (for whatever purpose—poetic, literal accuracy, et c.) without being stuffy or outdated.
Another factor in my naming it the probably #2, after Gilgamesh, though, is that everything else is just that bad to a modern reader, so the OT looks pretty damn good compared to all that, even if you're stuck with the King James Version. My favorite story from ancient Egypt[0], I wouldn't recommend to many readers, because damn, it's a slog, and it's still an easier read than some of the others, or than anything I've seen in Sumerian or Akkadian (Gilgamesh excepted). It probably tells better, as a joke (it's a comedic story), than it reads, if you had someone really talented telling it.
That's typical for other Near Eastern literatures, too. Lots and lots of repetition, is the main problem for a modern reader, as far as the prose goes. Much of it also doesn't really relate a story, exactly, and the cultural and religious references are obscure at best. You don't even get mythology, really, for the most part. Prayers or incantations, sure, but there's no Hesiod or Ovid of Sumerian religion. There's a little of that, sure, but it's very fragmentary and you have to bring a lot of context from outside of it to make much sense of what you're reading.
For the millennia(!) of texts we have from Egypt, for instance, there are only a few short (and often fragmentary) works that we'd recognize as stories. You have to settle for reading a variety of non-fiction or semi-fictional genres to get much more out of it—"mirrors for princes" and scribal didactic texts, which are probably the most interesting of the lot, plus endless formulaic and not-especially-illuminating funerary texts, and a good deal of historical propaganda about military victories, mostly from monumental inscriptions, almost all of which are intensely boring even if you're really into military history. And that's probably the richest literature we have from that region in the pre-classical period, at least as far as what's available in English translation.
[0] The Eloquent Peasant